Ms. Burns, the Xerox chief executive, says Mr. Icahn was not involved in the board’s decision to split the company in two, which was announced on Friday. But he is getting board seats at one offshoot while Ms. Burns, unusually, has not yet grabbed any role in the new structure.

Mr. Icahn agitated for the split and revealed a stake in Xerox last November. Ms. Burns told investors the previous month that the board was seriously considering strategic options for the company. Xerox suffers from shrinking sales in its photocopying and printing business, known as document technology, and from a steady decline in its stock price since late 2014.

Ms. Burns does have one problem relating to the new plan. Her defining bet in 2009, the same year she took the helm at Xerox, was to buy Affiliated Computer Services for $6.4 billion. This so-called business-process outsourcing operation – managing often paper-based administrative tasks for companies in health care, finance and other sectors – is now being separated again.

She may be right that seven years in business are like seven dog years: Things change quickly. But the reversal somewhat undermines her earlier judgment, and if nothing else may mean that it is time for leaders with new ideas at the two planned Xerox offshoots.

That said, corner-office occupants more often than not fit themselves into any significant corporate rejig. At Hewlett-Packard, whose split is something of a model for Xerox, the 2014 decision to separate into two companies came with news that Meg Whitman would continue as chief executive of one and chairwoman of the other. When eBay, another Icahn target, announced its divorce from PayPal the same year, it named two new chief executives but said its boss, John Donahoe, would remain on the board of one or both the companies.

Ms. Burns told Bloomberg TV that she “took discussion off the table” about her future. Assuming that’s the case, it may have helped Xerox’s board to focus on the business imperatives and the implications for shareholders. And it means directors can work out the details before deciding who is best suited to lead the new units, which sounds like the logical way around. Mr. Icahn may make more noise, but Ms. Burns’s shareholders-first approach is one that other corporate chiefs could emulate.